Mass-velocity dispersion relation using Gaia data and its effect on interpreting short-duration microlensing events

Thanks to the Gaia archived data, we find a correlation between the stellar types (with different average mass) and the scale parameters of the Maxwell-Boltzmann (MB) distribution of their dispersion velocities, by averaging over their age range. As expected, the late-type stars and brown dwarfs have wider velocity (MB) distributions with larger scale parameters than early-type ones. According to this correlation, we conclude that the dispersion velocities of brown dwarfs should have an MB profile with the scale parameter $a\simeq 111.9~\rm{km/s}$. This mass-velocity dispersion relation confirms the known age-velocity relation and additionally reveals the dependence of the stellar dispersion velocity to mass in the given average age. By considering this correlation as well as a brown dwarf population, we simulate microlensing events detectable by MOA-II toward the Galactic bulge fields gb5 and gb9 which were intensively observed during that observation. From this simulation, the average values of the events' duration are $18.72$ and $18.68~$days, which are close to the observational amounts, i.e., $17.4$ and $22.2~$days. In the simulation, we do not consider any extra free-floating exoplanet population. A population of speedy brown dwarfs with the corrected dispersion velocity profile generates the observational results of MOA-II and there is no need to include free-floating exoplanets.